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Reduced Power Rado's conjecture Prikry-type forcing Generalized Clubs square principles Singular cardinals combinatorics Antichain xbox Entangled linear order Universal Sequences Successor of Singular Cardinal Diamond for trees Large Cardinals Intersection model Martin's Axiom positive partition relation S-Space approachability ideal Uniformly coherent Dushnik-Miller Partition relations for trees full tree HOD Analytic sets GMA Small forcing Subadditive diamond star projective Boolean algebra Vanishing levels Knaster and friends Reflecting stationary set Souslin Tree Cohen real Subtle tree property Forcing Almost-disjoint family free Boolean algebra ccc Fat stationary set Coherent tree Subnormal ideal incompactness Parameterized proxy principle Whitehead Problem Microscopic Approach sap Kurepa Hypothesis Fodor-type reflection OCA weak square polarized partition relation unbounded function Ulam matrix Monotonically far regressive Souslin tree Almost countably chromatic Filter reflection Subtle cardinal Respecting tree Club Guessing Local Club Condensation. 54G20 Square-Brackets Partition Relations Amenable C-sequence Mandelbrot set Postprocessing function Precaliber Cardinal Invariants Hindman's Theorem Strongly Luzin set C-sequence Fast club Sierpinski's onto mapping principle coloring number Interval topology on trees Jonsson cardinal higher Baire space Poset Weakly compact cardinal Selective Ultrafilter stick Diamond Non-saturation Closed coloring Rainbow sets Ramsey theory over partitions Chang's conjecture Absoluteness Knaster PFA(S)[S] Distributive tree PFA Sigma-Prikry nonmeager set Commutative cancellative semigroups Slim tree weak Kurepa tree strongly bounded groups indecomposable filter Ineffable cardinal Forcing with side conditions Ostaszewski square transformations AIM forcing countably metacompact Ascending path Uniformization weak diamond very good scale Uniformly homogeneous Erdos-Hajnal graphs middle diamond Open Access Prevalent singular cardinals Diamond-sharp Greatly Mahlo Nonspecial tree tensor product graph Singular cofinality club_AD Hereditarily Lindelöf space Aronszajn tree b-scale Constructible Universe Axiom R Strongly compact cardinal Hedetniemi's conjecture Rock n' Roll Sakurai's Bell inequality O-space L-space Commutative projection system Chromatic number SNR square Luzin set Dowker space ZFC construction Strong coloring Iterated forcing Forcing Axioms stationary hitting Shelah's Strong Hypothesis Well-behaved magma Countryman line Lipschitz reduction free Souslin tree Was Ulam right? Singular Density perfectly normal reflection principles stationary reflection Partition Relations super-Souslin tree Erdos Cardinal Successor of Regular Cardinal Minimal Walks Almost Souslin Cardinal function specializable Souslin tree Ascent Path Foundations Generalized descriptive set theory P-Ideal Dichotomy
Tag Archives: Entangled linear order
Walks on uncountable ordinals and non-structure theorems for higher Aronszajn lines
Joint work with Tanmay Inamdar. Abstract. We investigate global structural properties of linear orders of a fixed infinite size. It is classical that the countable linear orders and the continuum-sized orders exhibit contrasting behaviours. Modern results show that strong extensions … Continue reading
Posted in Basis problems, Partition Relations, Preprints
Tagged Aronszajn tree, Ascending path, Club Guessing, Countryman line, Entangled linear order, Minimal Walks, Monotonically far, Partition relations for trees, Strong coloring, Subtle tree property, Vanishing levels, ZFC construction
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Strong failures of higher analogs of Hindman’s Theorem
Joint work with David J. Fernández Bretón. Abstract. We show that various analogs of Hindman’s Theorem fail in a strong sense when one attempts to obtain uncountable monochromatic sets: Theorem 1. There exists a colouring $c:\mathbb R\rightarrow\mathbb Q$, such that … Continue reading
Posted in Groups, Partition Relations, Publications
Tagged 03E02, 03E35, 03E75, 05A17, 05D10, 11P99, 20M14, Chang's conjecture, Commutative cancellative semigroups, Entangled linear order, Erdos Cardinal, Hindman's Theorem, Jonsson cardinal, Kurepa Hypothesis, Square-Brackets Partition Relations, Weakly compact cardinal, ZFC construction
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